Not really true. Sports books almost always require minimum bets and give drink tickets instead. You then hand the waitress/bartender your drink ticket in exchange for a free drink. You can't just sit there and watch the game and get free drinks.
You can usually get around this if you're clever, but it won't be completely free. Waitresses are usually instructed to serve free drinks to people who are betting on horses (bigger profits for the casinos than juice bets). If that's the case then just bet on around 5 horse races for $2 each and make sure you keep the bet slips in front of you at all times, even if they lose...usually the waitresses will see this and serve you free drinks the entire time. Just make absolutely sure you tip them every time.
Thats probably the best way to watch the game unless you don't gamble at all. Last time I was in vegas, and not during a major sporting even, we would go to the ESPN Zone in New York, New York...but I know back in 2010 it closed and reopened as another sports bar, so I'm not sure what's there now. Starting this Thursday though you won't even be able to stick your head into most places on the strip. The first weekend of March Madness is one of the craziest weekends of the year in Vegas. We usually just go downtown and avoid the strip when we want to bet/drink/watch games. The downtown casinos are older but they have decent sports books and cheap...everything
There used to be a sweet/affordable casino right on the strip called O'Sheas but it closed down a year or two ago. I have no idea what they replaced it with. edit: looks like it reopened although its a bit smaller than it used to be. They still have cheap games/drinks and beer pong though.